How do you find the exact value for #tan^-1(tan (7pi/4))#?

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Answer 1 · 2016-02-15T18:42:57

#kpi+3pi/4, k in ZZ#

#tan^-1(tan(7pi/4))#

By the trigonometric circle you can see that #tan(7pi/4)=tan(-pi/4)=-1#

So the expression simplifies in:

#tan^-1(-1)#

So which are the angles which tangent is -1?

Again by the trigonometric circle you can see that:

#tan^-1(-1)=kpi+3pi/4, k in ZZ#